Liverpool will move on to other transfer targets if they cannot conclude a deal for Southampton captain Adam Lallana soon, a source told ESPN FC.
The Merseysiders' 25 million pound offer for the 26-year-old remains on the table and their preference would be to finalise his signing soon.
But they are unwilling to raise their bid and believe the onus now lies with either Southampton or Lallana to determine what happens next.
Although Lallana is thought to be keen to move to Anfield, the midfielder is yet to submit a transfer request to force a move through.
Southampton, who have already sold striker Rickie Lambert to Liverpool, released a statement on Monday saying they wanted to put their transfer business on hold until they appoint a replacement to manager Mauricio Pochettino, who left to joint Tottenham.
It read: "Southampton Football Club can confirm that we have received multiple offers for some of our players in the past weeks. We have no need to accept any offers. We are deep in the process of appointing a new manager who will continue to move our club forward. It remains our preference not to partake in any transfers until the new manager is in place."
While a 25 million pound fee would be a club record, out-stripping the 12 million pounds they received from Arsenal for Alex Oxlade-Chamberlain in 2011, their position is complicated by a clause requiring them to pass on 25 percent of the proceeds of Lallana's sale to Bournemouth, whose Centre of Excellence he attended before joining Southampton.
Lallana is in England's World Cup squad and manager Roy Hodgson has said he is keen for his players to either resolve their future before they arrive in Brazil or to wait until after the tournament ends.
Liverpool are also targeting Sevilla left-back Alberto Moreno, with the Spanish club's president confirming the Reds' interest in the player on Tuesday.